What is the integral from 0 to 7 of t^3-9t^2+20t ?

The integral from 0 to 7 of t^3-9t^2+20t is 245/4

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integral from 0 to 7 of t^3-9t^2+20t

\int_{0}^{7} t^{3} - 9 t^{2} + 20 t d t

\frac{245}{4}

Decimal

61.25

Solution steps

\int_{0}^{7} t^{3} - 9 t^{2} + 20 t d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{7} t^{3} d t - \int_{0}^{7} 9 t^{2} d t + \int_{0}^{7} 20 t d t

\int_{0}^{7} t^{3} d t = \frac{2401}{4}

\int_{0}^{7} 9 t^{2} d t = 1029

\int_{0}^{7} 20 t d t = 490

= \frac{2401}{4} - 1029 + 490

Simplify

\frac{2401}{4} - 1029 + 490 : \frac{245}{4}

= \frac{245}{4}

What is the integral from 0 to 7 of t^3-9t^2+20t ?
The integral from 0 to 7 of t^3-9t^2+20t is 245/4